{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-02-23T14:18:37.782795Z",
     "start_time": "2024-02-23T14:18:37.413612Z"
    }
   },
   "source": [
    "\"\"\"\n",
    "linear regression with multiple variables\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def J_theta(theta, x, y):\n",
    "    m = len(y)\n",
    "\n",
    "    return np.sum((theta @ x - y) ** 2) / (2 * m)\n",
    "\n",
    "\n",
    "def updateTheta(theta, x, y, lr):\n",
    "    m = len(y)\n",
    "\n",
    "    gradient = lr * (1 / m) * np.sum((theta @ x - y) * x, axis=1)\n",
    "    return theta - gradient\n",
    "    # tmp = (theta @ x - y)\n",
    "    # return np.array([\n",
    "    #     theta[0] - lr * (1 / m) * np.sum(tmp * x0),\n",
    "    #     theta[1] - lr * (1 / m) * np.sum(tmp * x1)\n",
    "    # ])\n",
    "\n",
    "\n",
    "def linearRegression():\n",
    "    data2 = np.loadtxt(\"ex1data2.txt\", delimiter=\",\")\n",
    "\n",
    "    # normalize the first feature\n",
    "    x0_mean = np.mean(data2[:, 0])\n",
    "    x0_std = np.std(data2[:, 0])\n",
    "    data2[:, 0] = (data2[:, 0] - x0_mean) / x0_std\n",
    "\n",
    "    y = data2[:, 2]\n",
    "    x = data2[:, 0:2]\n",
    "    x = np.vstack((np.ones(len(y)), x.T))\n",
    "    \n",
    "\n",
    "    theta = np.zeros(x.shape[0])\n",
    "    lr = 0.1\n",
    "    iterations = 5000\n",
    "    \n",
    "    costs_x = []\n",
    "    costs = []\n",
    "    for i in range(iterations):\n",
    "        theta = updateTheta(theta, x, y, lr)\n",
    "        cost = J_theta(theta, x, y)\n",
    "        costs_x.append(i)\n",
    "        costs.append(cost)\n",
    "        print(\"iteration: {}, theta: {}, cost: {}\".format(i, [t for t in theta], cost))\n",
    "\n",
    "    \n",
    "    # predict\n",
    "    square = (1650 - x0_mean) / x0_std\n",
    "    bedrooms = 3\n",
    "    print(\"predict result: {}\".format(theta @ np.array([1, square, bedrooms]).T))\n",
    "    \n",
    "    # draw costs\n",
    "    plt.title(\"changes of costs\")\n",
    "    plt.plot(costs_x, costs, \"k\")\n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "linearRegression()"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration: 0, theta: [34041.26595744681, 10576.41334928156, 112036.77021276596], cost: 7221834108.622795\n",
      "iteration: 1, theta: [29160.365400633775, 15372.081681088654, 93886.19053971057], cost: 5475605698.445414\n",
      "iteration: 2, theta: [30521.674838406834, 20453.35223565405, 96351.29956232345], cost: 5200127158.591771\n",
      "iteration: 3, theta: [30965.361323106164, 24922.574803443033, 95553.4232926743], cost: 5002892310.843938\n",
      "iteration: 4, theta: [31617.622912905186, 28978.510967577407, 95273.5880987876], cost: 4841145207.457651\n",
      "iteration: 5, theta: [32293.37205412668, 32640.650451538495, 94913.08872485942], cost: 4707461589.503096\n",
      "iteration: 6, theta: [33015.8322529607, 35951.77346126595, 94566.72162858497], cost: 4596509866.538892\n",
      "iteration: 7, theta: [33775.85217094301, 38946.38587359369, 94219.47184773159], cost: 4503988433.568143\n",
      "iteration: 8, theta: [34569.95566595082, 41656.17595935566, 93873.71235154354], cost: 4426413299.3820505\n",
      "iteration: 9, theta: [35394.26192833449, 44109.56312568271, 93529.06285995875], cost: 4360962322.65288\n",
      "iteration: 10, theta: [36245.39878628008, 46332.14087035584, 93185.57906707044], cost: 4305349450.773234\n",
      "iteration: 11, theta: [37120.3136289425, 48346.94099349721, 92843.24764851546], cost: 4257722863.5304008\n",
      "iteration: 12, theta: [38016.26333066782, 50174.6926769283, 92502.06622368217], cost: 4216582469.733457\n",
      "iteration: 13, theta: [38930.77983307201, 51834.052284647274, 92162.03069416991], cost: 4180713079.4823575\n",
      "iteration: 14, theta: [39861.64318288967, 53341.81071702761, 91823.13724861007], cost: 4149130273.7008243\n",
      "iteration: 15, theta: [40806.85663046687, 54713.079945080295, 91485.38204516521], cost: 4121036558.452748\n",
      "iteration: 16, theta: [41764.624319059294, 55961.46090467449, 91148.76126175311], cost: 4095785849.9333158\n",
      "iteration: 17, theta: [42733.33118927844, 57099.194599218936, 90813.27108804384], cost: 4072854707.30665\n",
      "iteration: 18, theta: [43711.52489563031, 58137.298092412544, 90478.90772667703], cost: 4051819031.299207\n",
      "iteration: 19, theta: [44697.89953101435, 59085.686901668625, 90145.66739301936], cost: 4032335190.055325\n",
      "iteration: 20, theta: [45691.28097884933, 59953.28515220691, 89813.54631515323], cost: 4014124731.075194\n",
      "iteration: 21, theta: [46690.61372999029, 60748.12471573686, 89482.54073382914], cost: 3996961997.8795843\n",
      "iteration: 22, theta: [47694.94901796883, 61477.43443527467, 89152.64690242392], cost: 3980664099.503312\n",
      "iteration: 23, theta: [48703.43414072266, 62147.720427480264, 88823.86108689816], cost: 3965082785.779983\n",
      "iteration: 24, theta: [49715.30285016566, 62764.83835476247, 88496.179565754], cost: 3950097866.317749\n",
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      "iteration: 26, theta: [51746.507275364886, 63860.124157827035, 87844.1145830741], cost: 3921545776.490355\n",
      "iteration: 27, theta: [52764.66915872618, 64347.30461924857, 87519.7237408719], cost: 3907835420.1470304\n",
      "iteration: 28, theta: [53783.85365266226, 64799.4422911288, 87196.42243163481], cost: 3894428755.7408004\n",
      "iteration: 29, theta: [54803.61309098415, 65219.99552127665, 86874.20699594368], cost: 3881283514.453489\n",
      "iteration: 30, theta: [55823.54573423551, 65612.07697698931, 86553.07378667014], cost: 3868365355.049051\n",
      "iteration: 31, theta: [56843.29117312291, 65978.48821258525, 86233.01916893553], cost: 3855646358.3270016\n",
      "iteration: 32, theta: [57862.52619161617, 66321.75078018567, 85914.03952006965], cost: 3843103807.625048\n",
      "iteration: 33, theta: [58880.961043751624, 66644.13422941958, 85596.13122956976], cost: 3830719201.0215936\n",
      "iteration: 34, theta: [59898.336102768175, 66947.68130716008, 85279.29069905977], cost: 3818477451.215177\n",
      "iteration: 35, theta: [60914.418845342625, 67234.23063728871, 84963.51434224944], cost: 3806366237.422254\n",
      "iteration: 36, theta: [61929.00113741439, 67505.43713248514, 84648.79858489383], cost: 3794375480.409872\n",
      "iteration: 37, theta: [62941.896791440646, 67762.79036483951, 84335.13986475284], cost: 3782496917.267634\n",
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      "iteration: 4939, theta: [368114.0183081742, 109447.79367639736, -8738.012709014005], cost: 2043280050.6028368\n",
      "iteration: 4940, theta: [368114.01837872504, 109447.79368577903, -8738.012730520852], cost: 2043280050.6028373\n",
      "iteration: 4941, theta: [368114.01844903897, 109447.7936951292, -8738.012751955437], cost: 2043280050.602837\n",
      "iteration: 4942, theta: [368114.0185191167, 109447.79370444798, -8738.012773318062], cost: 2043280050.6028368\n",
      "iteration: 4943, theta: [368114.01858895906, 109447.79371373545, -8738.012794608921], cost: 2043280050.6028368\n",
      "iteration: 4944, theta: [368114.0186585668, 109447.79372299172, -8738.01281582828], cost: 2043280050.6028361\n",
      "iteration: 4945, theta: [368114.0187279408, 109447.7937322169, -8738.012836976355], cost: 2043280050.602836\n",
      "iteration: 4946, theta: [368114.0187970818, 109447.79374141111, -8738.012858053404], cost: 2043280050.6028364\n",
      "iteration: 4947, theta: [368114.0188659905, 109447.79375057443, -8738.012879059663], cost: 2043280050.6028368\n",
      "iteration: 4948, theta: [368114.0189346678, 109447.79375970698, -8738.012899995361], cost: 2043280050.602836\n",
      "iteration: 4949, theta: [368114.01900311443, 109447.79376880886, -8738.012920860752], cost: 2043280050.6028361\n",
      "iteration: 4950, theta: [368114.0190713312, 109447.79377788016, -8738.012941656052], cost: 2043280050.602836\n",
      "iteration: 4951, theta: [368114.01913931884, 109447.79378692099, -8738.012962381516], cost: 2043280050.602836\n",
      "iteration: 4952, theta: [368114.01920707815, 109447.79379593146, -8738.012983037377], cost: 2043280050.6028368\n",
      "iteration: 4953, theta: [368114.01927460986, 109447.79380491166, -8738.013003623862], cost: 2043280050.6028364\n",
      "iteration: 4954, theta: [368114.01934191474, 109447.7938138617, -8738.013024141192], cost: 2043280050.6028354\n",
      "iteration: 4955, theta: [368114.01940899354, 109447.79382278168, -8738.013044589608], cost: 2043280050.6028361\n",
      "iteration: 4956, theta: [368114.0194758471, 109447.7938316717, -8738.013064969347], cost: 2043280050.6028361\n",
      "iteration: 4957, theta: [368114.01954247605, 109447.79384053187, -8738.01308528064], cost: 2043280050.6028361\n",
      "iteration: 4958, theta: [368114.01960888127, 109447.79384936228, -8738.01310552371], cost: 2043280050.602836\n",
      "iteration: 4959, theta: [368114.01967506343, 109447.79385816302, -8738.013125698799], cost: 2043280050.602836\n",
      "iteration: 4960, theta: [368114.0197410233, 109447.7938669342, -8738.013145806117], cost: 2043280050.602836\n",
      "iteration: 4961, theta: [368114.01980676164, 109447.79387567592, -8738.013165845901], cost: 2043280050.6028352\n",
      "iteration: 4962, theta: [368114.0198722792, 109447.79388438829, -8738.013185818376], cost: 2043280050.6028354\n",
      "iteration: 4963, theta: [368114.01993757667, 109447.79389307139, -8738.013205723779], cost: 2043280050.6028352\n",
      "iteration: 4964, theta: [368114.0200026548, 109447.79390172532, -8738.013225562308], cost: 2043280050.602835\n",
      "iteration: 4965, theta: [368114.0200675144, 109447.7939103502, -8738.013245334208], cost: 2043280050.6028354\n",
      "iteration: 4966, theta: [368114.02013215615, 109447.7939189461, -8738.0132650397], cost: 2043280050.6028352\n",
      "iteration: 4967, theta: [368114.0201965808, 109447.79392751314, -8738.013284679024], cost: 2043280050.602835\n",
      "iteration: 4968, theta: [368114.020260789, 109447.7939360514, -8738.013304252376], cost: 2043280050.602835\n",
      "iteration: 4969, theta: [368114.0203247816, 109447.79394456098, -8738.013323759977], cost: 2043280050.6028354\n",
      "iteration: 4970, theta: [368114.02038855926, 109447.79395304198, -8738.013343202056], cost: 2043280050.6028345\n",
      "iteration: 4971, theta: [368114.0204521227, 109447.79396149449, -8738.01336257885], cost: 2043280050.6028352\n",
      "iteration: 4972, theta: [368114.0205154727, 109447.79396991862, -8738.013381890562], cost: 2043280050.6028352\n",
      "iteration: 4973, theta: [368114.0205786099, 109447.79397831445, -8738.013401137405], cost: 2043280050.6028352\n",
      "iteration: 4974, theta: [368114.020641535, 109447.79398668208, -8738.013420319614], cost: 2043280050.602835\n",
      "iteration: 4975, theta: [368114.0207042488, 109447.79399502161, -8738.01343943738], cost: 2043280050.6028352\n",
      "iteration: 4976, theta: [368114.02076675196, 109447.79400333313, -8738.013458490956], cost: 2043280050.6028354\n",
      "iteration: 4977, theta: [368114.02082904516, 109447.79401161673, -8738.013477480521], cost: 2043280050.6028345\n",
      "iteration: 4978, theta: [368114.02089112916, 109447.79401987251, -8738.0134964063], cost: 2043280050.602835\n",
      "iteration: 4979, theta: [368114.0209530046, 109447.79402810056, -8738.013515268529], cost: 2043280050.602835\n",
      "iteration: 4980, theta: [368114.02101467224, 109447.79403630097, -8738.013534067386], cost: 2043280050.6028352\n",
      "iteration: 4981, theta: [368114.0210761328, 109447.79404447385, -8738.013552803113], cost: 2043280050.6028345\n",
      "iteration: 4982, theta: [368114.02113738685, 109447.79405261927, -8738.01357147592], cost: 2043280050.602835\n",
      "iteration: 4983, theta: [368114.0211984352, 109447.79406073733, -8738.013590085993], cost: 2043280050.6028342\n",
      "iteration: 4984, theta: [368114.0212592785, 109447.79406882812, -8738.01360863358], cost: 2043280050.6028345\n",
      "iteration: 4985, theta: [368114.02131991746, 109447.79407689175, -8738.013627118857], cost: 2043280050.6028342\n",
      "iteration: 4986, theta: [368114.02138035273, 109447.79408492829, -8738.013645542045], cost: 2043280050.6028342\n",
      "iteration: 4987, theta: [368114.021440585, 109447.79409293784, -8738.013663903354], cost: 2043280050.6028345\n",
      "iteration: 4988, theta: [368114.02150061505, 109447.79410092048, -8738.013682203], cost: 2043280050.602835\n",
      "iteration: 4989, theta: [368114.02156044345, 109447.79410887632, -8738.01370044119], cost: 2043280050.6028337\n",
      "iteration: 4990, theta: [368114.0216200709, 109447.79411680544, -8738.013718618122], cost: 2043280050.602835\n",
      "iteration: 4991, theta: [368114.0216794981, 109447.79412470793, -8738.013736734005], cost: 2043280050.6028337\n",
      "iteration: 4992, theta: [368114.02173872566, 109447.79413258386, -8738.013754789035], cost: 2043280050.6028352\n",
      "iteration: 4993, theta: [368114.0217977543, 109447.79414043335, -8738.013772783426], cost: 2043280050.6028337\n",
      "iteration: 4994, theta: [368114.02185658464, 109447.79414825648, -8738.013790717376], cost: 2043280050.6028337\n",
      "iteration: 4995, theta: [368114.02191521745, 109447.79415605332, -8738.013808591088], cost: 2043280050.6028337\n",
      "iteration: 4996, theta: [368114.0219736533, 109447.79416382399, -8738.013826404778], cost: 2043280050.6028333\n",
      "iteration: 4997, theta: [368114.0220318929, 109447.79417156854, -8738.013844158622], cost: 2043280050.6028345\n",
      "iteration: 4998, theta: [368114.0220899369, 109447.7941792871, -8738.013861852864], cost: 2043280050.6028337\n",
      "iteration: 4999, theta: [368114.02214778593, 109447.79418697972, -8738.013879487653], cost: 2043280050.6028345\n",
      "predict result: 293081.46388582006\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 54
  },
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     "end_time": "2024-02-23T14:13:46.407427Z",
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   "source": [
    "\n",
    "\"\"\"\n",
    "Regular equations\n",
    "正规方程求theta\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "\n",
    "data2 = np.loadtxt(\"ex1data2.txt\", delimiter=\",\")\n",
    "\n",
    "# # normalize the first feature\n",
    "# x0_mean = np.mean(data2[:, 0])\n",
    "# x0_std = np.std(data2[:, 0])\n",
    "# data2[:, 0] = (data2[:, 0] - x0_mean) / x0_std\n",
    "\n",
    "y = data2[:, 2]\n",
    "x = data2[:, 0:2]\n",
    "x = np.vstack((np.ones(len(y)), x.T))\n",
    "\n",
    "theta = (np.linalg.pinv(x.T @ x) @ x.T).T @ y\n",
    "print(\"theta: {}\".format(theta))\n",
    "\n",
    "# predict\n",
    "print(\"predict result: {}\".format(theta @ np.array([1, 1650, 3]).T))\n",
    "\n"
   ],
   "id": "e48a114c5da6bd80",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta: [89597.90963335   139.21067403 -8738.01914598]\n",
      "predict result: 293081.4643490739\n"
     ]
    }
   ],
   "execution_count": 41
  },
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   "cell_type": "code",
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   "execution_count": null,
   "source": "",
   "id": "90140ae8e11793fa"
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   "source": "",
   "id": "8819ba40a4731cb5",
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   "execution_count": null
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   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "d14cd849c13ceeb6"
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